Question

Match each polynomial in standard form to its equivalent factored form.

Standard forms:
8x^3+1
2x^4+16x
x^3+8

the equivalent equation that would match with it
(x+2)(x2−2x+4)
The polynomial cannot be factored over the integers using the sum of cubes method.
(2x+16)(4x^2−32x+64)
(x+1)(4x^2−2x+1)
2x(x+2)(x^2−2x+4)
(x+8)(x^2−16x+64)
(2x+1)(4x^2−2x+1)

For equation 1) 8x^3+1 I believe the matching product is (x+8)(x^2−16x+64)
For equation 2) (2x+16)I believe the matching product is (4x^2−32x+64)
For equation 3) x^3+8 I believe the matching product is (x+1)(4x^2−2x+1)

I am not really sure at all I am struggling with this subject

Answer 1

8x^3+1 = (2x)^3 + 1^3 = ((2x)+1)((2x)^2 - (2x)(1) + 1^2)
= (2x+1)(4x^2-2x+1)

2x^4+16x = 2x(x^3+1) = 2x(x+1)(x^2-x+1)

x^3+8 = x^3 + 2^3 = ...

Answer 2

would the third one be (x+2)(x2−2x+4)

Answer 3

or The polynomial cannot be factored over the integers using the sum of cubes method.

Answer 4

your factoring is correct.
sum and difference of cubes can always be factored.

Answer 5

2x^4+16x = 2x(x^3+1) = 2x(x+1)(x^2-x+1)
Is not a choice I am confused.

Answer 6

Yeah I was looking at that and was wondering of I messed up some where